Automorphism group of the balanced hypercube

Abstract

Huang and Wu in [IEEE Transactions on Computers 46 (1997), pp. 484–490] introduced the balanced hypercube BHn as an interconnection network topology for computing systems. In this paper, we completely determine the full automorphism group of the balanced hypercube. Applying this, we first show that the n-dimensional balanced hypercube BHn is arc-transitive but not 2-arc-transitive whenever n ≥ 2. Then, we show that BHn is a lexicographic product of an n-valent graph Xn and the null graph with two vertices, where Xn is a Z2n − 1-regular cover of the n-dimensional hypercube Qn.